"Time to Fusion", "Ion-Ion Collision Time&quo

[mattman]

Hello,

I have the following question about the following formulas. Feel Free to chime in here If I have something wronge.


1. How long does it take an ion inside an isotropic plasma to
fuse? Rider provides the formula as:

Time to fusion = 1/(effective density of plasma * <Cross section of
reaction * Velocity collisions> )



2. How long does it take ions to collide inside an isotropic
plasma? From Rider's paper:

ion-ion Collision time = [3*SQRT(3) * SQRT(Mass Ion) * Temperature of
Plasma^(3/2)] / [8* Pi * Charge on the ion^4 * e^4 * effective density
of ions * Columbic Logarithm ]



3. How long will an ion travel alone before encountering the field
of another ion? Well, we know that the columbic logarithm gives us
the mean free path inside a plasma, so...

Free Flying Ion Time = Ion Velocity(time) * Columbic Logarithm



Feel free to disagree with anything I have written so far. Now we
can put this all together, because the 3 times should be linked inside
the polywell. Since to fuse, two ions must collide, then it would
seem that “time to fusion” should be some multiple of “ion-ion
collision time”. Say an ion has 300 collisions with other ions, and
on the last collision it fuses – in that case the “time to fusion”
should be roughly 300 times the “ion-ion collision time”. That
relation should hold, except there are times when an ion is moving
alone. So mathematically can I roughly say the following:


Time to fusion == N * ion-ion Collision time + M * Free Flying Ion Time


Now statistically there are a great number of ions inside the
polywell which would not fuse. So the above expression only holds for
maybe... say, 1 in 1000 ions inside the polywell. For the rest, the
other 999 ions Time to fusion is infinity. In their case, we might
consider a "Time to Loss" expression. Incidentally rider compares the
"Time to Fusion" and the "Ion-Ion Collision time" and uses it as the
underpinnings for his argument that the polywell will thermalize
faster then it produces energy. Anyone have any arguments on this?

[chrismb]

Yup. All sounds about right.

Problem is... around here this is fighting-talk because most of the folks who have blind faith in the-word-of-Nebel reject any such analysis.

It's pretty straightforward; fusion cross-section is calculated on the basis that mean free path is 1/[density].[cross-section], so folks do their collider experiments and get a value for cross-section from the probability of collisions, in a given column-length of target nucleii, versus density, and work backwards.

What those fusion cross-sections tell us is that multi-10's keV ions have to travel for millions of miles before they get to any reasonable chance of fusion probability.

I've written a few posts with numbers in on this stuff. Try; viewtopic.php?p=36507#36507

[D Tibbets]

Without looking up formula or numbers, some possibly relevant items dragged from memory.

Mean distance to fusion in a Tokamac (or Tokamak) may be ~ 300,000 KM (from Chrismb- about 2/3rds of the way to the Moon) and requires ~ 800 seconds- which would give the ions a speed of ~ 400,000 M/s- which I assume is similar to an average energy of ~ 5 KeV. [EDIT- actually this is probably closer to ~ 10-15KeV for the high energy tail of the thermalized plasma in a Tokamak where the average energy is closer to 5 KeV.]

Ion lifetime in a Polywell may be ~ 20 ms or less. Traveling at ~ 1 million M/s, that would be ~ 20 kilometers traveled. I believe Bussard claimed that most of the ions would fuse within this time frame. Compared to a Tokemak, the density MIGHT be as much as ~ 1000-10,000 times greater. The fusion rate scales as the density squared, so the relative time frames and distances traveled are reasonable, even when the ~ 100 fold slower D-D fusion rate is taken into account. Also, the fusion rate of the total ion population is considerably different when most of the ions are at the chosen energy as opposed to a thermalized plasma where only the high energy tail is at this chosen energy.

Rider's conclusions are reasonable, but perhaps skewed. Chacon's (sp?) Fokker- Plank (sp?) calculations may be more relevant. Also, ANNEALING needs to be considered. This is one of the claimed properties of the Polywell that is essential to delaying full thermalization within the ion lifetimes. This not only effects the fusion rate, but also the Bremsstrulung losses, which I believe was one of Rider's major concerns, especially for high Z fuels like boron11. And, the spherical shape of the reaction space and dynamic motions of the ions need to be considered. When the ions approach the center they are most dense and scattering collisions would be most frequent, but only upscattering and downscattering collisions occur in the center as any deflection from the center of a sphere does not add angular momentum. This slows the angular momentum or transverse thermalization, while the annealing impeads the radial thermalization. These two effects are what impedes excessive thermalization over the required lifetime.* And, finally, unlike a ignition machine like a Tokamak where the fusion products heats the plasma, in Polywells, these fusion products naturally leave without heating the plasma.

At least this is my understanding of the counter arguments to Rider's conclusions.

* This assumes significant confluence of the ions towards the center. This is desirable, but Dr Nebel claimed it is not essential. In this case the plasma would have random angular momentum, but apparently the energy spread of the ions would still be adequately impeded by annealing.
The absolutely critical element (along with controlling the dominant electron power losses) of the Polywell is the Wiffleball confinement, and the tremendous density advantage that this imparts. I suspect many of the comparisons do not assume much confluence, as this would effectively increase the fusion rate further, perhaps to impressive rates. In the 2008 patent application, Bussard, etel even claimed that the confluence (central focus) could be theoretically so great that all of the ions would fuse on their first pass through the core. In this case the ion lifetimes might be on the order of less than a microsecond- no thermalization worries there, or rather the ions in this tiny core would very quickly thermalize as the coulomb collisions still far exceed the fusion collisions, but still the ions fuse before they can escape this dense core. I think a more realistic intermediate confluence performance would allow for significantly smaller sizes and/ or required B-field strengths. Of course, such impressive performance may place intolerable heat loads on the machine surfaces. But, this illustrates, that at least in theory, the size and performance of these machines may be limited by thermal loads, not the physics of fusion.
An alternative to good confluence due to the basic dynamics of the machine, might be to incorporate POPS techniques.

Dan Tibbets

[D Tibbets]

Somewhat off topic, but if POPS does work in a spherical geometry, I wounder if it could be applied to a cylindrical, or by extension, a toroidal geometry?

Dan Tibbets

[Stoney3K]

I wounder if it could be applied to a cylindrical, or by extension, a toroidal geometry?

You could always propose the idea at JET or IGNITOR to give it a shot.

It would be pretty cool to hear that one of those beat the break-even point before their bigger ITER sister fires first plasma.

"Sorry guys, you can send the trucks home, that big honkin' kettle isn't needed anymore. We did it already."

[happyjack27]

Somewhat off topic, but if POPS does work in a spherical geometry, I wounder if it could be applied to a cylindrical, or by extension, a toroidal geometry?

Dan Tibbets

i'd be concerned about instability. not only do you have non-convex fields, but you have an entire continum -- namely, about the major circumference -- for variations and spatial feedback effects among them to occur. an inherent difficulty with the toroidal symmetry approach.

[KitemanSA]

1. How long does it take an ion inside an isotropic plasma to fuse?
2. How long does it take ions to collide inside an isotropic plasma?

Are properly functioning Polywell plasmas "isotropic"? Wouldn't the desired dominant radial component to the ions provide a non-isotropic plasma?

[D Tibbets]

1. How long does it take an ion inside an isotropic plasma to fuse?
2. How long does it take ions to collide inside an isotropic plasma?

Are properly functioning Polywell plasmas "isotropic"? Wouldn't the desired dominant radial component to the ions provide a non-isotopic plasma?

Probably not. Even if considerable thermalization occurs in the direction (not energy) there is always a new stream of nearly radial ions entering the machine (at least in steady state mode). If there is greater confluence because directional thermalization (if that's an appropriate word to use- as it is direction, not energy that we are talking about) lags significantly behind the rate of new ion injection, then vertual anode formation, parabolic potential wells and possibly other factors changes the dynamics in the system. I take the baseline (worst case) Polywell plasma as being (almost) isotropic when Nebel mentioned that the Polywell would work without confluence. Even in glow discharge Fusors with a lot more neutrals around, there has been found to be central virtual anode formation in some tests.

Dan Tibbets

[happyjack27]

i'm not sure what "isotropic" means, but in the sims its clear that if you start ions w/two different charge-to-mass ratios off with the same position and ke distribution, they will arrive at the center at different times because the lower charge-to-mass one takes longer to accelerate. so if fusion must be between these two different species (e.g. D-T fusion or P-b11 fusion), it won't happen at all on the first couple of passes through the center. one has to wait until their relative phases diffuse (i.e. they "mix") until you'll start seeing fusion. this happens pretty quickly, though, in my sims (a few picohours).

i supose before this happens though, you'll still get the species passing by each other, but it won't be in the center, it will be in a sphere (or spheres, depending on how many passes) about the center, so it will be in a region less dense than the center.

i wonder if POPS would cause their phases to separate out again, causing the expected radius that they pass by each other to be >0? this could actually hurt the net fusion rate, esp. given that its proportional to density _squared_, and density is a decreasing function of radius.

[D Tibbets]

If the machine operated for only a few passes and was operated in a extreamely short pulse mode, this might apply. But the ion input is essentially two hoses spurting out ions continuously. The first protons would win the race to the center, but the boron would be close behind, and all of the following ions of each species would be mixed together thereafter. IE: the dynamic would be a continuous stream of both particles except for the first tiny amount of time represented by the time of flight differences. This discrepancy would be washed out quickly as the run times are thousands to billions (or more) times or longer. Also mutual scattering and momentum exchange would mix them up in other ways. In other words, this would be a major consideration in single (or a few passes machine) but the Polywell is perhaps a 10-20,000 pass machine.

Dan Tibbets

[mattman]

Guys, I am sorry it takes me so long to respond to anything on this forum. For example I am STILL working on responses to Dan Tibbets, Chrismbs and kcdodd comments from the first week in November. I have written 11 pages. But I am having trouble writing about brillouin limits.

I have found many, many papers on leon brillouin's work. Including brillouin limits, brillouin flow, brillouin zones. I spent a few days side tracked reading papers on plasma drift, and brillouin limits in tokomaks, stellerators, ect... I am sorry I am taking so long. I want you guys to know I am not ignoring this feedback.

[chrismb]

Matt, the Brillouin limit should be taken with a pinch of salt when interpreting fusion plasmas, especially with beam-type reactors. You may like to look up the 'Penning fusion experiment'. If you look more widely still, you will find that under some circumstances the Brillouin limit has been measured as exceeded by a factor of 40, whereas in other cases some setups can only reach a fraction of that.

In any case, the basis of your question/thread seemed to evolve from you trying to understanding whether there was any prospect of fusion reactions happening quicker than thermalisation reactions. The answer is actually very simple;

a) use a thermal plasma [generally hot], and that way there are no 'lossy' ion collisions as the energy is kept in (because it is already all 'thermal')
b) use a beam-type device [generally cold, locally hot] but make sure that the hot ions are pulled back up to their principal energy so that they do not diffuse down in velocity-space.
c) if not a nor b, then no.

As Dan mentions above, there is a posited idea that Polywell will have some 'annealing' process at the edge that re-distributes energy there, thereby keeping ions at the same energy. Problem is, ions have to get to the edge, and if they coulomb-scatter anywhere other than the centre, then one of them is unlikely to make it back to the edge. But my speculations on it working are only speculations, just as the speculations that there will be such a process are speculations and, currently, are nothing more than speculations.

It seems you may have read Rider's thesis. Whether or not you have done so, go revisit it and take a good read of 'Appendix E'.

Rider does not claim that there are no such 'b' processes, merely that he hasn't seen it [in Polywell, or otherwise]. But he still goes ahead and puts forward the bare-bones of a few ways to achieve 'b'. The problem is that you are resisting entropy changes if you are aiming to maintain a generally cold locally hot configuration, and that takes energy one way or the other.

In any case, my own experiment is a 'b' type device and it is essentially one that Rider put in his Appendix, in section E2.2. He is aware of my work, but as he appears to have given up on fusion science (and moved into bio-tech) I think he has some, justifiable, disillusionment over the whole fusion venture.

[MSimon]

Yup. All sounds about right.

Problem is... around here this is fighting-talk because most of the folks who have blind faith in the-word-of-Nebel reject any such analysis.

It's pretty straightforward; fusion cross-section is calculated on the basis that mean free path is 1/[density].[cross-section], so folks do their collider experiments and get a value for cross-section from the probability of collisions, in a given column-length of target nucleii, versus density, and work backwards.

What those fusion cross-sections tell us is that multi-10's keV ions have to travel for millions of miles before they get to any reasonable chance of fusion probability.

I've written a few posts with numbers in on this stuff. Try; viewtopic.php?p=36507#36507

If the plasma is not isotropic the formulas are useless.

[chrismb]

If the plasma is not isotropic the formulas are useless.

I think you'll find they are still relevant, though they become only oom approximations.

The reality of essentially all plasma experiments is that in the end, formulas have been useless for just about all fusion science! Formulas provide a prospective interpretation of what might be, it is found to be wrong [I've never heard of a prediction being exactly right!], and then the formulas are adjusted to fit that which is observed.

We have yet to get any real data from Polywell that we can even begin to go through this iterative process. It may be a position to take, then, to say "then all is still possible" and I would not be in disagreement with that. The issue I have is the 25 years of research on it already, and nothing that can be given to any external parties to the proceedings that would permit independent analysis. As tax-payer funded work, I find this wholly unsatisfactory.

But this is diverting the thread. Let me please urge everyone to read Appendix E of Rider's thesis, before he is condemned as the ultimate cynic!

[icarus]

Plural of "formula" is "formulae".

Latin.